Fast numerical generation and encryption of computer-generated Fresnel holograms
Summary (2 min read)
1. Introduction
- Numerical generation and encryption of holographic data are two important topics in the realm of holography that have instigated numerous research works in the past two decades.
- Basically, heavy computation is involved in the hologram generation process, and the addition of numerical encryption will further lower the computation efficiency.
- Second, the authors employed the set of 1D maximum length sequence (M-sequence) [24] as the key signals.
- The decryption process can be achieved with numerical means with a small amount of arithmetic operations.
- The vast difference between the reconstructed form of an encrypted hologram that has been decodedwith, andwithout, the right encryption key is illustrated.
A. Fast Generation of Fresnel Holograms
- Given a set of 3D, self-illuminating object points.
- Without loss of generality, the authors assumed that the source image has identical size and resolution as the hologram.
- Compared with the direct implementation in Eq. (1), the alternative hologram generation method based on Eqs. (4) and (5) is significantly faster as it only involves a pair of one-dimensional processes, i.e., the formation of the diffraction pattern Oðx; τÞ in each scan plane and the subsequent generation of the overall diffraction pattern Dðx; yÞ.
- The authors further noted that Oðx; τÞ can be derived with an economical hardware solution based on field programmable gate array (FPGA) at a throughput of over 100M pixels per second [25].
B. Fast Encryption of Holograms
- The authors now propose to encrypt the hologram generated with Eq. (5) by convolving the conversion signal RðyÞ with a one-dimensional binary M-sequence signal.
- In fact, with the prime polynomial, the authors can generate the M-sequence.
- Subsequently, a new bit value is shifted to the output of the shift register.
- As the formation of Oðx; yÞ can be realized with the hardware solution, the computation loading on this part of the process is not taken into account.
3. Experimental Evaluation
- The authors shall evaluate their method with the standard image “Lenna” shown in Fig.
- The mean square error (MSE) is 3196, and the peak signal to noise ratio (PSNR) is 13:1dB, indicating an extremely low coding fidelity.
- Next the encrypted hologram is decrypted with the same encryption key S1ðyÞ, and the reconstructed image is shown in Fig. 4(c).
- The encryption method can be conducted with an encryption key of longer M-sequences.
- It can be seen that apart from a slight blurriness, together with minor ringing at the boundary and the junction between the upper and lower sections, the reconstructed images at each section are similar to the original one.
4. Conclusion
- The authors have proposed a method for fast numerical generation and encryption of a Fresnel hologram.
- This effectively merges the generation and encryption process into a single entity.
- First, the amount of complexity involved in the generation of the hologram is significantly smaller than that employing the direct table lookup technique.
- Experimental results reveal that the visual quality of a reconstructed image from a hologram that is generated and encrypted by their method is extremely poor, if not beyond recognition, if it is obtained without decrypting the hologram with the correct key.
- The latter can be integrated with existing image encryption schemes, such as [2–8] to foster stronger resistance of optical images towards illegal access and attacks.
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Citations
Cites background or methods from "Fast numerical generation and encry..."
...The complex amplitude of the proposed method is described by the formula (2), which has higher contrast than the traditional hologram....
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...Assume that / T f b λ = , equation (2) further can be expressed by...
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Additional excerpts
...Gabor in 1940s [1], has become a very popular technique applied in numerous fields involving microscopy [2, 3], 3-D imaging [4, 5], encryption [6-8] and so on....
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References
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"Fast numerical generation and encry..." refers background or methods in this paper
...Second, we employed the set of 1D maximum length sequence (M-sequence) [24] as the key signals....
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...According to [24], the autocorrelation function of each member in theM-sequence is close toa train ofKroneckerdelta function....
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...Mathematically, the latter can be expressed as the primitive (prime) polynomial [24]...
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